Question

) A mixture of liquid alkanes, being stored at 15.00°C, contains n-hexane, cyclopentane, and isoheptane. Data on these alkanes is provided below.

Alkane	Formula	Amount (w/w%)	ΔHvap (kJ/mol)	P* at 20.00°C (kPa)
n-hexane	C6H14	42.4%	31.11	16.44
cyclopentane	C5H10	56.1%	28.86	34.61
isoheptane	C7H16	1.5%	34.89	5.300

a) What is the saturated vapour pressure, in kPa, of each pure component at 15.00°C?

b) What is the vapour pressure of each component, in kPa, above the liquid mixture at equilibrium?

c) What is the mole fraction (y) of each component in the vapour phase above the liquid mixture at equilibrium?

d) The isoheptane is removed from the mixture during an extraction process, leaving behind a mixture of just n-hexane and cyclopentane. The vapour-liquid equilibrium data for this mixture are shown below (temperature in °C vs. mole fraction of n-hexane). What percentage of a 35% n-hexane mixture is in the liquid phase at 144°C?

Answer 1

The no. of moles of n-hexane = 42.4/86 = 0.493 mol

The no. of moles of cyclopentane = 56.1/70 = 0.801 mol

The no. of moles of isoheptane = 1.5/100 = 0.015 mol

The total no. of moles = 0.493+0.801+0.015 = 1.309 mol

Part A.

According to Clausius-Cleyperon equation:

ln(P^*/P1) = H_vap/R (1/T1 - 1/T2)

i.e. ln(P2/16.44) = 31.11*1000/8.3145 (1/293.15 - 1/288.15)

i.e. P^* = 13.17 kPa for n-hexane

Now, ln(P^*/34.61) = 28.86*1000/8.3145 (1/293.15 - 1/288.15)

i.e. P^* = 28.18 kPa for cyclopentane

Finally, ln(P^*/5.3) = 34.89*1000/8.3145 (1/293.15 - 1/288.15)

i.e. P^* = 4.13 kPa for isoheptane

Part B.

Vapour pressure of n-hexane = (no. of moles of hexane/total no. of moles) * P^*

= (0.493/1.309)*13.17

= 4.96 kPa

Vapour pressure of cyclopentane = (no. of moles of cyclopentane/total no. of moles) * P^*

= (0.801/1.309)*28.18

= 17.24 kPa

Vapour pressure of isoheptane = (no. of moles of isoheptane/total no. of moles) * P^*

= (0.015/1.309)*4.13

= 0.05 kPa

Part C.

Total pressure = 4.96+17.24+0.05 = 22.25 kPa

The mole fraction of n-hexane in the vapor phase = vapor pressure of n-hexane/total pressure

= 4.96/22.25

= 0.223

The mole fraction of cyclopentane in the vapor phase = vapor pressure of cyclopentane/total pressure

= 17.24/22.25

= 0.775

The mole fraction of isoheptane in the vapor phase = vapor pressure of isoheptane/total pressure

= 0.05/22.25

= 0.002